A wave on a string is described by y(x,t)=( 4.0 cm )×cos[2π(x/( 2.4 m )+t/( 0.30...

A wave on a string is described by y(x,t)=( 4.0 cm )×cos[2π(x/( 2.4 m )+t/( 0.30 s ))] , where x is in m and t is in s. Part B What is the wave speed? Express your answer in meters per second. Part C What is the wave frequency? Express your answer in hertz. Part D What is the wave length? Express your answer in meters. Part E At t = 0.75 s , what is the displacement of the string at x = 0.20 m ? Express your answer in centimeters.

Solutions

Expert Solution

We know that

y(x,t) =A cos(kx+wt). ....1

part B) We know that the wave speed

v=w/k

comparing equation 1 from the given equation so w=2/T=2/0.30s , k=2/ =2/2.4 m

v=(2/0.30s)/(2/2.4 m)

v=8.0 m/s answer

part C) The wave frequency

f=1/T

f=1/0.30

f =3.33 Hz

part D) As you know , k=2/ =2/2.4 m

=2.4 m Answer

part E)

y(x,t)=( 4.0 cm )×cos[2π(x/( 2.4 m )+t/( 0.30 s ))]

here x=0.20 m , t=0.75 s

y(x,t)=( 4.0 cm )×cos[2π(0.20/( 2.4 m )+0.75/( 0.30 s ))]

y(x,t)=-3.464 cm

genius_generous answered 1 year ago

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